The Communication Map of a Transformer

arXiv:2608.22007v2 Announce Type: replace-cross Abstract: The components of a transformer communicate by writing to and reading from a shared residual stream, and the mechanistic interpretability literature has mapped these connections by hand, one circuit at a time. We present the communication map, which charts every potential communication channel from the geometry of the model's weights alone, generalizing the composition score of Elhage et al. (2021) into a single coupling coefficient covering all 18 connection classes, from head-to-head to neuron-to-neuron and everything in between. We provide an account of the properties of the coupling coefficient, including its geometric interpretation and its exact chance level. The census finds that 70-89% of head pairs are oriented far from chance, some coupled strongly and others actively avoiding each other. We demonstrate the communication map in two novel applications. In Application 1, we recover the known induction circuits blind from the strongest head-to-head couplings and group the heads into communities, and ablating one such community destroys the model's in-context copying. In Application 2, we pool the coupling coefficients of every head to identify a distinct two-dimensional residual stream subspace, whose deletion abolishes the induction capability in six models up to Pythia-6.9B. We show that this subspace is different from those identified by either activation PCA or outlier dimensions. We release the map, the statistical machinery, and the intervention suite.